When Behind Leapfrog

In HBR Magazine, Apr-12, the cover story is about Leadership Lessons of Steve Jobs.

One of the 14 keys: When Behind Leapfrog. In short is is a about the first iMacs the have lacked burning CDs. This seems to have led to iTunes, iTunes Store and the iPods(simplified).

Only those technical computing systems that are built atop systems like Mathematica, Maple, .. have symbolic computation capabilities that enable the combination of symbolic and numerical techniques to solve, say, SDEs, PDEs, PIDEs, ... adequately, fast and robust. Do symbolic manipulations to make them of good nature for numerical treatment, might be a key.

The European Extremely Large Teslescope (E-ELT) will go into operation in 2020 and will then, with its 40 meter mirror,  be the largest ground-based telescope on earth. The Austrian Adaptive Optics Team (consisting of MathConsult, RICAM and the Industrial Math Institute - MathConsult also makers of UnRisk and partners of us in computational finance) have been and are developing the mathematical algorithms for deblurring the deep space images by deformable mirrors. For certain applications in Adaptive Optics, these algorithms are 100- 1000 times faster than conventional methods and can therefore adjust the mirror on a kilohertz scale. On contemporary PCs.

But facing the new computing muscles such algorithms might run millions of times faster and enable a completely new range of applications. But programming paradigms will also change to massive data and massive thread techniques.  Will we then still need our good  old friends, the special functions, mathematical objects and operators?  Or solve by one-for-all kind of brute force algorithms?

Will those who grow up with this computing muscles leapfrog to simplified and reduced code and outperform existing solutions?

We, at UnRisk, are in the process of reinventing UnRisk.
To run portfolio-across-scenario analytics in record time we have optimized numerical schemes, and drive CUDA systems over grids (controlled by Mathematica).
But this kernel code will be rebuilt from scratch.
One kernel C code will run on all future heterogeneous CPU/GPU architectures and valuation and data management will be inherently parallel.

Because we are not behind, we would not need to leapfrog, but  we decided this reverse innovation anticipating a paradigm shift in scientific and technical computing.